Chapter 4: Q. 12 (page 215)

Find the remaining zeros of $f (x)$ with real coefficients and given information.
The degree is 5 and zeros are $0, 1, 2, i$

Short Answer

Expert verified

The remaining zero of the polynomial is $- i$ .

Step by step solution

Step 1. Given Information

The polynomial has degree 5 and four zeros are $0, 1, 2, i$ .

Step 2. Concept

Conjugate Pair Theorem says that if a polynomial with degree $n$ with real coefficient, has one complex zero of the form $a + i b$ then the polynomial should have the conjugate pair of $a + i b$ that is $a - i b$ as another zero.

Step 3. Explanation

Since the function has coefficients that are real numbers, complex zeros appear as conjugate pairs.

It follows that $- i$ , the conjugate of $i$ is the remaining zero.

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Find the remaining zeros of $f (x)$ with real coefficients and given information.
The degree is 5 and zeros are $0, 1, 2, i$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept

Step 3. Explanation

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Find the remaining zeros of fxwith real coefficients and given information.The degree is 5 and zeros are0,1,2,i

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept

Step 3. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Geometry

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find the remaining zeros of $f (x)$ with real coefficients and given information.
The degree is 5 and zeros are $0, 1, 2, i$